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Preprint volume - SIBM

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Pre-print Volume –Posters<br />

Topic 4: THE ELASMOBRANCHS<br />

between 1 and 3. Modelling studies indicate that optimal Lévy flight search patterns<br />

occur with μ~2 (Viswanathan et al., 1999, 2000).<br />

Results - While some final analyses are still being drawn together, it is clear from our<br />

early results on basking shark, bigeye tuna, blue sharks, white tip sharks, leatherback<br />

turtle and Magellanic penguin that Lévy behaviour is present. We found exponents for<br />

individuals of these species with μ close to the optimum of 2. Although the analysis is<br />

not yet complete some interesting differences have been identified between species. In<br />

particular the billfish and the bigeye thresher shark have Lévy exponents close to 1.<br />

These species perform diel vertical migrations (Sedberry and Loefer, 2001; Nakano et<br />

al., 2003), resulting in long vertical displacements as they travel to and from deep<br />

water which produce low Lévy exponents. It is an interesting confirmation of the<br />

statistical methods that these known behavioural differences have been correctly<br />

identified.<br />

Conclusions – Using electronic tag data recording the diving movements of large<br />

marine predators such as sharks and tunas, we show evidence for the presence and<br />

diversity of Lévy behaviour. This provides the most comprehensive and convincing<br />

support for the idea that organism search strategies evolved to exploit optimal Lévy<br />

searches.<br />

References<br />

BRADSHAW C.J.A., SIMS D.W., HAYS G.C. (2007) - Measurement error causes scale-dependent<br />

threshold erosion of biological signals in animal movement data. Ecological Applications,<br />

17:628-638.<br />

CLAUSET A., SHALIZI C.R., NEWMAN M.E.J. (2009) - Power-Law Distributions in Empirical<br />

Data. Siam Review, 51: 661-703.<br />

NAKANO H., MATSUNAGA H., OKAMOTO H., OKAZAKI M. (2004) - Acoustic tracking of<br />

bigeye thresher shark Alopias superciliosus in the eastern Pacific Ocean. Marine Ecology-<br />

Progress Series, 265: 255-261.<br />

SEDBERRY G.R., LOEFER J.K. (2001) - Satellite telemetry tracking of swordfish, Xiphias gladius<br />

off the eastern United States. Marine Biology, 139: 355-360.<br />

SIMS D.W., RIGHTON D., PITCHFORD J.W. (2007) - Minimising errors in identifying Lévy flight<br />

behaviour of organisms., 76: 222-229.<br />

SIMS D.W., SOUTHALL E.J., HUMPHRIES N.E., HAYS G.C., BRADSHAW C.J.A.,<br />

PITCHFORD J.W., JAMES A., AHMED M.Z., BRIERLEY A.S., HINDELL M.A., MORRITT<br />

D., MUSYL M.K., RIGHTON D., SHEPARD E.L.C., WEARMOUTH V.J., WILSON R.P.,<br />

WITT M.J., METCALFE J.D. (2008) - Scaling laws of marine predator search behaviour.<br />

Nature, 451: 1098-1102.<br />

VISWANATHAN G.M., AFANASYEV V., BULDYREV S.V., HAVLIN S., DA LUZ M.G.E.,<br />

RAPOSO E.P., STANLEY H.E. (2000) - Lévy flights in random searches. Physica, A 282: 1-12.<br />

VISWANATHAN G.M., BULDYREV S.V., HAVLIN S., DA LUZ M.G.E., RAPOSO E.P.,<br />

STANLEY H.E. (1999) - Optimizing the success of random searches. Nature, 401: 911-914.<br />

VISWANATHAN G.M., RAPOSO E.P., DA LUZ M.G.E. (2008) - Lévy flights and superdiffusion in<br />

the context of biological encounters and random searches. Physics of Life Reviews, 5: 133-150.<br />

41 st S.I.B.M. CONGRESS Rapallo (GE), 7-11 June 2010<br />

229

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